Such a safety device is known from the European Published Patent Appln. No. EP 1 738 882 A2. In the known safety device, two sensor devices are provided that are independent of each other, of which one sensor device is situated as a tactile sensor device on the gripping arm of an industrial robot, while the other sensor device is developed particularly as a capacitive sensor device, which records a close range about the industrial robot, for instance, a range within 10 cm about the sensor device. This means that the last named sensor device first responds when an object or a person is located at a distance of a moving gripping device that is less than 10 cm. The first named sensor device even first responds only when there has been a collision or touching between the object and the gripping device. The safety device known from European Published Patent Appln. No. 1 738 882 A2 therefore operates particularly safely, to be sure, based on the redundant or duplicated execution of the sensor devices, but early detection of objects approaching the industrial robot, that leads to a targeted speed reduction or collision avoidance between the object and the gripping device is not possible using the previously known safety device. Therefore, the traversing speed of the robot for the safe avoidance of collisions is limited by the range of the close range sensor and the braking distance of the robot.